Deductive Logic Part 3

-- 82. A Quality is an attribute which does not require more than one substance for its existence. The attributes just mentioned are qualities. There might be greenness, hardness, and weight, if there were only one green, hard and heavy substance in the universe.

-- 83. A Relation is an attribute which requires two or more substances for its existence, e.g. nearness, fatherhood, introduction.

-- 84. When we say that a substance can be conceived to exist by itself, what is meant is that it can be conceived to exist independently of other substances. We do not mean that substances can be conceived to exist independently of attributes, nor yet out of relation to a mind perceiving them. Substances, so far as we can know them, are only collections of attributes. When therefore we say that substances can be conceived to exist by themselves, whereas attributes are dependent for their existence upon substances, the real meaning of the a.s.sertion reduces itself to this, that it is only certain collections of attributes which can be conceived to exist independently; whereas single attributes depend for their existence upon others. The colour, smoothness or solidity of a table cannot be conceived apart from the extension, whereas the whole cl.u.s.ter of attributes which const.i.tutes the table can be conceived to exist altogether independently of other 'such cl.u.s.ters. We can imagine a table to exist, if the whole material universe were annihilated, and but one mind left to perceive it. Apart from mind, however, we cannot imagine it: since what we call the attributes of a material substance are no more than the various modes in which we find our minds affected.

-- 85. The above division of things belongs rather to the domain of metaphysics than of logic: but it is the indispensable basis of the division of terms, to which we now proceed.

CHAPTER III.

_Of the Division of Terms._

-- 86. The following scheme presents to the eye the chief divisions of terms.

Term Division of terms according to their place in thought.

Subject-Term Attributive

according to the kind of thing signified.

Abstract Concrete

according to Quant.i.ty in Extension.

Singular Common

according to Quality.

Positive Privative Negative

according to number of meanings.

Univocal Equivocal

according to number of things involved in the name.

Absolute Relative

according to number of quant.i.ties.

Connotative Non-connotative

_Subject-term and Attributive._

-- 87. By a Subject-term is meant any term which is capable of standing by itself as a subject, e.g. 'ribbon,' 'horse.'

-- 88. Attributives can only be used as predicates, not as subjects, e.g. 'cherry-coloured,' 'galloping.' These can only be used in conjunction with other words (syncategorematically) to make up a subject. Thus we can say 'A cherry-coloured ribbon is becoming,' or 'A galloping horse is dangerous.'

-- 89. Attributives are contrivances of language whereby we indicate that a subject has a certain attribute. Thus, when we say 'This paper is white,' we indicate that the subject 'paper' possesses the attribute whiteness. Logic, however, also recognises as attributives terms which signify the non-possession of attributes. 'Not-white' is an attributive equally with 'white.'

-- 90. An Attributive then may be defined as a term which signifies the possession, or non-possession, of an attribute by a subject.

-- 91. It must be carefully noticed that attributives are not names of attributes, but names of the things which possess the attributes, in virtue of our knowledge that they possess them. Thus 'white' is the name of all the things which possess the attribute whiteness, and 'virtuous' is a name; not of the abstract quality, virtue, itself, but of the men and actions which possess it. It is clear that a term can only properly be said to be a name of those things whereof it can be predicated. Now, we cannot intelligibly predicate an attributive of the abstract quality, or qualities, the possession of which it implies. We cannot, for instance, predicate the term 'learned' of the abstract quality of learning: but we may predicate it of the individuals, Varro and Vergil. Attributives, then, are to be regarded as names, not of the attributes which they imply, but of the things in which those attributes are found.

-- 92. Attributives, however, are names of things in a less direct way than that in which subject-terms may be the names of the same things. Attributives are names of things only in predication, whereas subject-terms are names of things in or out of predication. The terms 'horse' and 'Bucephalus' are names of certain things, in this case animals, whether we make any statement about them or not: but the terms 'swift' and 'fiery' only become names of the same things in virtue of being predicable of them. When we say 'Horses are swift' or 'Bucephalus was fiery,' the terms 'swift' and 'fiery' become names respectively of the same things as 'horse' and 'Bucephalus.' This function of attributives as names in a secondary sense is exactly expressed by the grammatical term 'noun adjective.' An attributive is not directly the name of anything. It is a name added on in virtue of the possession by a given thing of a certain attribute, or, in some cases, the non-possession.

-- 93. Although attributives cannot be used as subjects, there is nothing to prevent a subject-term from being used as a predicate, and so a.s.suming for the time being the functions of an attributive. When we say 'Socrates was a man,' we convey to the mind the idea of the same attributes which are implied by the attributive 'human.' But those terms only are called attributives which can never be used except as predicates.

-- 94. This division into Subject-terms and Attributives may be regarded as a division of terms according to their place in thought. Attributives, as we have seen, are essentially predicates, and can only be thought of in relation to the subject, whereas the subject is thought of for its own sake.

_Abstract and Concrete Terms_.

-- 95. An Abstract Term is the name of an attribute, e.g. whiteness [Footnote: Since things cannot be spoken of except by their names, there is a constantly recurring source of confusion between the thing itself and the name of it. Take for instance 'whiteness.' The attribute whiteness is a thing, the word 'whiteness' is a term.], multiplication, act, purpose, explosion.

-- 96. A Concrete Term is the name of a substance, e.g. a man, this chair, the soul, G.o.d.

-- 97. Abstract terms are so called as being arrived at by a process of Abstraction. What is meant by Abstraction will be clear from a single instance. The mind, in contemplating a number of substances, may draw off, or abstract, its attention from all their other characteristics, and fix it only on some point, or points, which they have in common. Thus, in contemplating a number of three-cornered objects, we may draw away our attention from all their other qualities, and fix it exclusively upon their three-corneredness, thus const.i.tuting the abstract notion of 'triangle.' Abstraction may be performed equally well in the case of a single object: but the mind would not originally have known on what points to fix its attention except by a comparison of individuals.

-- 98. Abstraction too may be performed upon attributes as well as substances. Thus, having by abstraction already arrived at the notion of triangle, square, and so on, we may fix our attention upon what these have in common, and so rise to the higher abstraction of 'figure.' As thought becomes more complex, we may have abstraction on abstraction and attributes of attributes. But, however many steps may intervene, attributes may always be traced back to substances at last. For attributes of attributes can mean at bottom nothing but the co-existence of attributes in, or in connection with, the same substances.

-- 99. We have said that abstract terms are so called, as being arrived at by abstraction: but it must not be inferred from this statement that all terms which are arrived at by abstraction are abstract. If this were so, all names would be abstract except proper names of individual substances. All common terms, including attributives, are arrived at by abstraction, but they are not therefore abstract terms.

Those terms only are called abstract, which cannot be applied to substances at all. The terms 'man' and 'human' are names of the same substance of which Socrates is a name. Humanity is a name only of certain attributes of that substance, namely those which are shared by others. All names of concrete things then are concrete, whether they denote them individually or according to cla.s.ses, and whether directly and in themselves, or indirectly, as possessing some given attribute.

-- 100. By a 'concrete thing' is meant an individual Substance conceived of with all its attributes about it. The term is not confined to material substances. A spirit conceived of under personal attributes is as concrete as plum-pudding.

-- 101. Since things are divided exhaustively into substances and attributes, it follows that any term which is not the name of a thing capable of being conceived to exist by itself, must be an abstract term. Individual substances can alone be conceived to exist by themselves: all their qualities, actions, pa.s.sions, and inter-relations, all their states, and all events with regard to them, presuppose the existence of these individual substances. All names therefore of such things as those just enumerated are abstract terms. The term 'action,' for instance, is an abstract term. For how could there be action without an agent? The term 'act' also is equally abstract for the same reason. The difference between 'action' and 'act' is not the difference between abstract and concrete, but the difference between the name of a process and the name of the corresponding product. Unless acts can be conceived to exist without agents they are as abstract as the action from which they result.

-- 102. Since every term must be either abstract or concrete, it may be asked--Are attributives abstract or concrete? The answer of course depends upon whether they are names of substances or names of attributes. But attributives, it must be remembered, are never directly names of anything, in the way that subject-terms are; they are only names of things in virtue of being predicated of them. Whether an attributive is abstract or concrete, depends on the nature of the subject of which it is a.s.serted or denied. When we say 'This man is n.o.ble,' the term 'n.o.ble' is concrete, as being the name of a substance: but when we say 'This act is n.o.ble,' the term 'n.o.ble'

is abstract, as being the name of an attribute.

-- 103. The division of terms into Abstract and Concrete is based upon the kind of thing signified. It involves no reference to actual existence. There are imaginary as well as real substances. Logically a centaur is as much a substance as a horse.

_Terms._

-- 104. A Singular Term is a name which can be applied, in the same sense, to one thing only, e.g. 'John,' 'Paris,' 'the capital of France,' 'this pen.'

-- 105. A Common Term is a name which can be applied, in the same sense, to a cla.s.s of things, e.g. 'man,' 'metropolis,' 'pen.'

In order that a term may be applied in the same sense to a number of things, it is evident that it must indicate attributes which are common to all of them. The term 'John' is applicable to a number of things, but not in the same sense, as it does not indicate attributes.

-- 106. Common terms are formed, as we have seen already (-- 99), by abstraction, i. e. by withdrawing the attention from the attributes in which individuals differ, and concentrating it upon those which they have in common.

-- 107. A cla.s.s need not necessarily consist of more than two things. If the sun and moon were the only heavenly bodies in the universe, the word 'heavenly body' would still be a common term, as indicating the attributes which are possessed alike by each.